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Binary01.ppt
DecimalDecimal: Base 10 means 10 Unique numerical digits
0 1 2 3 4 5 6 7 8 9
1 1 1 1 1
1101001,00010,000Weight Positions
3, 4 6 710
3 x 1000 = 3000
4 x 100 = 400
6 x 10 = 60
7 x 1 = 7
------------------------
3,467
etc.
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Binary01.ppt
DecimalAddition
0 1 2 3 4 5 6 7 8 9
3
+ 5--------- 8 start +1 +2 +3 +4 +5
6
+ 7--------- 13
0 1 2 3 4 5 6 7 8 9
start +1 +2 +3+6 +7+4 +5
Carry 1
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Binary01.ppt
BinaryDecimal: Base 2 means 2 Unique numerical digits
0 1 On Off In Out Left Right
1 1 1 1 1 1
12 4 816Decimal Weight Positions
32etc.
1 0 1 1 0 12
1 x 32 = 32
0 x 16 = 0
1 x 8 = 8
1 x 4 = 4
0 x 2 = 0
1 x 1 = 1
------------------------
4510
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Binary01.ppt
BinaryAddition
0+ 0------ 0
1+ 0------ 1
0+ 1------ 1
1
1 + 1 ------ 1 0with a 1 carry
1 0 1 1 0 1 0 1 1
0 0 1 0 0 1 0 0 1
1 1 0 1 1 0 1 0 0
1 1 1 1 Carry
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Binary01.ppt
HexadecimalDecimal: Base 16 means 16 Unique numerical digits
0 1 2 3 4 5 6 7 8 9
A B C D E F
Decimal Equivalents
0 = 0
1 = 1
2 = 2
3 = 3
4 = 4
5 = 5
6 = 6
7 = 7
8 = 8
9 = 9
A = 10
B = 11
C = 12
D = 13
E = 14
F = 15
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Binary01.ppt
Hexadecimal
0-F 0-F 0-F 0-F 0-F 0-F
1,048,576 65,536 4,096 256 16 1
Decimal Weight Positions
A 3 9 D 6 C16
A = 10 X 1,048,576 = 10,485,760
+ 3 = 3 X 65,536 = 196,608
+ 9 = 9 X 4096 = 36,864
+ D = 13 X 256 = 3,328
+ 6 = 6 X 16 = 96
+ C = 12 X 1 = 12
------------------------------------------------------
10,722,66810
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Binary01.ppt
Hexadecimalto Binary
0 = 0000
1 = 0001
2 = 0010
3 = 0011
4 = 0100
5 = 0101
6 = 0110
7 = 0111
8 = 1000
9 = 1001
A = 1010
B = 1011
C = 1100
D = 1101
E = 1110
F = 1111
It takes 4 bits to make one Hex number
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Binary01.ppt
Octal
Decimal: Base 8 means 8 Unique numerical digits
0 1 2 3 4 5 6 7
Decimal Equivalents
0 = 0
1 = 1
2 = 2
3 = 3
4 = 4
5 = 5
6 = 6
7 = 7
Octal to Binary
0 = 000
1 = 001
2 = 010
3 = 011
4 = 100
5 = 101
6 = 110
7 = 111
It takes 3 bits to make one Octal number
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Binary01.ppt
1 1 1 1
1864512
Decimal Weight Positions
Octal
7 5 2 38
7 x 512 = 3,584
16 x 5 = 80
2 x 8 = 16
3 x 1 = 3
-------
3,68310
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Binary01.ppt
Binary to Decimal
1 0 1 1 0 1 0 1
Decimal Weights128 32 16 4 1 = 18110
Add the decimal weights of the “1” bits
Decimal to Binary1. Find the largest binary bit that will fit in the number without going over the number
2. Mark that bit as “on” and subtract the bit weight value from the decimal number
3. Repeat steps 1 and 2 until there are no more numbers remaining in the decimal number
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Binary01.ppt
Hex to Binary
C 5 9 B16
1100 0101 1001 10112 11000101100110112=
Convert Hex to Binary
Binary to HexDivide bits into groups of 4
11000101100110112
C 5 9 B16
1.
2.
3.
1100 0101 1001 10112
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Binary01.ppt
Binary to OctalDivide bits into groups of 3
11000101100110112
1 4 2 6 3 38
1.
2.
3.
1 100 010 110 011 0112
Octal to Binary1 4 2 6 3 38
001 100 010 110 011 0112
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Binary01.ppt
Hex to Octal to DecimalBreak the hex or octal or decimal number into binary
1 0 1 1 1 0 0 0 1 0 1 1
2048 512 256 128 8 2 1
Decimal: add the weights = 2,95510
Hexadecimal: divide the bits into patterns of 4 = B8B16
Octal: divide the bits into patterns of 3 = 56138